Let $V=CC'$ ($dim(C)=(n,k),k<n$) be a symmetric $(n,n)$ real matrix produced from unknown full-rank matrices C. I want to decompose it uniquely into the product $AA'$, $dim(A)=(n,k)$. What limitations are enough to put on A, so that the decomposition is unique within that class? I would appreciate any hints in the direction of the solution.
2026-03-27 02:07:35.1774577255
Conditions for the unique symmetric matrix decomposition
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